performance of stepper motor axes · 2020. 8. 4. · stepper motor controllers with more microsteps...

WHITE PAPER – Performance of Stepper Motor Axes

– Joachim Oberfell, Birgit Schulze –

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany of 11 Phone +49 721 4846-0, Fax +49 721 4846-1019, Email [email protected], www.pi.ws

Performance of Stepper Motor Axes

Optimization of Precision, Stability, and Repeatability

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WHITE PAPER – Performance of Stepper Motor Axes -- Joachim Oberfell, Birgit Schulze --


1 Drive Technology Basics

Irrespective of the business sector or the market, a produc-

tion process that is not based on moving components from

one position to the other is inconceivable.

Positioning tasks of this type are increasingly being taken over

by machines and automated procedures ensure safety and

reproducibility. Reliable drives with the corresponding life-

time are essential for this purpose. At the same time, the

demand on positioning precision in the industrial environ-

ment is also increasing.

On the following pages, it will be shown how positioning

systems with a stepper motor drive can be used in precision

positioning, and also what special properties they have.

Rotating electric motors are a typical and widespread solution

for drive technology in the industrial sector. Stepper motors

are usually preferred because they are considered to be

particularly robust and have a long lifetime. The have a high

torque even at low speed = velocity. They are also attractively

priced and can be operated by affordable controllers. Stepper

motors heat up during (continuous) operation and this must

be taken into account when designing a system.

Stepper motors take discrete positions within one revolution.

Because these steps have a constant distance, a position may

be commanded using the number of steps without the need

for a position sensor. Normally, there are 200 to 500 full steps

in each revolution. The actual achievable step size is deter-

mined by the stepper motor control, which, depending on the

version, electronically interpolates up to several thousand

microsteps between the full steps.

When holding a position, stepper motors are very stable,

particular the full steps. For this purpose, current must be

continually applied to stepper motors without a self-locking

gearhead.

PI uses smooth-running 2-phase stepper motors for the posi-

tioning axes in high-precision mechanics. A mechanical

damper on the motor shaft, which also works as handwheel,

supports smooth running. A combination of suitable linear

measuring systems and high-resolution controllers increases

the positioning repeatability.

Fig. 1 Examples of PI precision axes with stepper motor: L-509 linear

axis (former PLS-85), L-511 linear axis (former LS-110), L-611 rota-

tion stages (former PRS-110), L-310 Z-axis stage (former ES-100),

MCS XY stage (from above)


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2 Precision Positioning into the

Nanometer Range

A stepper motor with 200 full steps per revolution rotates at

an angle of 1.8° for each step. This results in a feed of 10 µm

in conjunction with a drive screw with a pitch of 1 mm. The

position resolution that could be theoretically achieved is

calculated (without further mechanical gear reduction) from

the number of microsteps in each full step, which the motor

controller interpolates. A controller, with for example,

256 microsteps, achieves a design position resolution of

39 nm, which corresponds to 625 nm at 16 microsteps. The

steps that are commanded in the mechatronic system and

can be cleanly executed are limited to whole number multi-

ples of this calculated resolution.

Fig. 2 Steps of an L-511 linear stage with 2-mm drive screw, which is

controlled by a motor controller with 16 microsteps per full step. 3-

µm steps (left), 0.6-µm steps (right)

Stepper motor controllers with more microsteps between the

full steps such as for example, the SMC Hydra (3000 mi-

crosteps), achieve a corresponding finer division of the motor

rotation angle. They allow virtually stepless position com-

manding, even in small and very small steps. This results in

particularly smooth-running motors, a very high position

resolution, uniform feed, and a higher dynamic velocity and

acceleration range. The efficiency of these controllers is very

high, which suppresses heating up of the motors.

Systems with these types of high-resolution stepper motor

controllers are therefore theoretically able to achieve position

resolutions into the nanometer range. This allows actual

measured and typical step sizes in the range of a few na-

nometers, which are only limited by the mechanical charac-

teristics of the positioning axis. Due to the high design resolu-

tion, virtually any step sizes are possible. Fig. 3 and 4 are

examples of 100 nm and 25 nm steps of an L-509 axis with 1

mm spindle pitch.

Fig. 3 100-nm steps of an L-509 linear stage with 2-phase stepper

motor, and without position control


motor, and without position control


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3 Optimizing the Repeatability

with Position Control

A stepper motor executes uniform steps reliably with high-

precision repeatability. The repeatability of a position that has

been reached once in an overall mechatronic system also

depends on the mechanical components and their interac-

tion: The coupling and possibly the gearhead, drive screw,

drive screw nut, and the guidings used, determine the me-

chanical play. These mechanical effects of the construction

can never be completely eradicated.

The accuracy, with which a position is reached each time, can

be improved by additional position feedback and evaluation

in the controller. A direct-measuring linear or angle measur-

ing system in the desired resolution effectively suppresses the

mechanical backlash/play. At the same time, the linearity of a

measuring system is normally higher than that of the motor

so even here, there is room for improvement.

Fig. 5 to 9 show the step sizes of an L-511 axis with 2-mm

spindle pitch, recorded during control. In this case, step sizes

up to 20 nm are easily verifiable.


motor, and with position control (10 kHz sample frequency, unfil-tered)

Fig. 6 Detail view of Fig. 5 (zoom)


motor, and with position control


motor, and with position control

Fig. 9 10-nm steps of an L-511 linear stage with 2-phasen stepper

motor, with position control. The 10-nm steps can still be differenti-

ated, but are no longer executed cleanly


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3.1 Stability and Resolution in Control

Position-controlled stepper motor axes are distinguished by

an excellent position stability. Why is that the case?

Classical (DC) servo systems exhibit typical controller oscilla-

tion at amplitudes within the range of the resolution. De-

pending on the servo parameters, they can reach multiples of

the resolution and even lead to the total instability of the

system. These effects do not occur with stepper motors.

Initially a stepper motor does not need control for position

stability. As soon as current is applied to the motor, it builds

up a moment while it is at a standstill. In contrast to (DC)

servo systems, it has an intrinsic velocity servo control ("ve-

locity feedforward"). These are the ideal requirements for

excellent stability. Common stepper motor controllers, with

for example, 256 microsteps per full step, allow smooth con-

trol of discrete step sizes. The commandable positions are

limited to whole number multiples of the theoretical resolu-

tion. Any step sizes within a range of a few tens of nanome-

ters are however, not possible, and a disparity between the

motor and the encoder resolution leads to a quantization of

the achievable positions.

Stepper motor controllers with more microsteps allow virtual-

ly stepless position commanding, even in small and very small

steps. The maximum accuracy is achieved when the position

signals are transmitted as analog sine-cosine signals with

1 Vpp and then digitized in the controller with a high resolu-

tion. The position resolution of such a positioning system is

only limited by the sensor.

3.2 Settling Behavior at the Position

The step-and-settle of an axis decisively affects the process

execution times. Initially, the control algorithms in the con-

troller influence the step-and-settle at the target position.

SMC controllers suppress high frequencies and still allow

dynamic positioning with only minimal overshoot. The axis

therefore does not generate any oscillation that in return

could be registered by the overall system.

In order to achieve the shortest possible settling times, the

operating parameters must be optimized according to the

specifications of the application. The mass of the payload, the

resulting moments, and the orientation of the motion axis

must definitely be taken into account. Further measures are

not necessary; the system is stable, and optimized dynamical-

ly.

Fig. 10 1-mm steps, executed by an L-511 with position control

(velocity 15 mm/s; acceleration 200 mm/s2)

Fig. 11 The enlarged view from fig. 10 shows the very low oscillation

of less than 10 µm

Fig. 12 Further enlargements: It is clear to see that only one single

oscillation occurs. The target position was reached within a few

tenths of a second within a window of less than 20 nm


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4 Constant Velocity at Low Veloc-

ity

Velocity is a decisive parameter for selecting a positioning

system. Often, the fastest possible motion and positioning are

the most important factors. However, some applications

require particularly slow and even feed motion. Particularly

the velocity constancy presents a challenge.

The required velocities can range from a few 100 µm/s to

considerably less than 100 nm/s. This corresponds to a feed

of a few millimeters per day. For optimum and even motion, a

positioning system is recommended with a high-resolution

measuring system and with position resolutions of around a

nanometer.

Fig. 13 Velocity constancy at 1 µm/s, measured using an L-511 with

position control

Fig. 14 The measurement from fig. 13 in an enlarged view. The peri-

odic position deviation shown in the range of only a few nanometers

can be attributed to the interferometer

Fig. 15 Velocity constancy at 50 nm/s, measured using an L-511 with

position control

Fig. 16 Enlarged view of the measurement in fig. 15


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Background: How does the number of microsteps influence the positioning characteristics of an axis?

Velocity constancy

With only a few microsteps per full step, each step is particularly noticeable at very slow velocities. This is illustrated initially in the path-time diagram, where steps are clearly visible when suitably enlarged (fig. 17 and 18).

Operating at 3000 microsteps per full step, the path-time diagram shows very smooth almost perfect straighten (fig. 19 and 20) and therefore a considerably improved velocity con-stancy.

If measuring is repeated with position control, almost per-fect straightness is visible in the path-time diagram. Position deviation can be reduced to less than 100 nm by using the encoder (fig. 21 and 22)!

L-511 linear axis and C-663.11 Mercury Step motion controller (16 microsteps per full step). Velocity 5 µm/s

L-511 linear axis and SMC Hydra motion controller (3000 microsteps per full step). Velocity 5 µm/s

L-511 linear axis with measuring system (linear encoder) and SMC Hydra motion controller (3000 microsteps per full step). Velocity 5 µm/s

Fig. 17 Without position control (open-loop)

Fig. 19 Without position control (open-loop)

Fig. 21 With position control (closed-loop)

Fig. 18 Detailed view of Fig. 17 shows a distinct step

Fig. 20 Detailed view of Fig. 19

Fig. 22 Detailed view of Fig. 21


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Background: How does the number of microsteps influence the positioning characteristics of an axis? (cont.)

Position deviation and frequency behavior

If an axis is operated by a controller with fewer microsteps per full step, a position deviation around 1 µm amplitude is shown (fig. 23).

Residual oscillation of the mechanics results in higher frequencies and therefore increased resonance (fig. 24).

A controller with more microsteps per full step reduces both the absolute position deviation and the frequency spectrum considerably (fig. 25 and 26).

With the higher microstepping ratio, resonance now only occurs with 100 nanometer amplitude, a reduction to less than 10 % (fig. 27 and 28).

L-511 linear axis and C-663.11 Mercury Step motion controller (16 microsteps per full step). Velocity 5 µm/s

L-511 linear axis and SMC Hydra motion controller (3000 microsteps per full step). Velocity 5 µm/s

L-511 linear axis with measuring system (linear encoder) and SMC Hydra motion controller (3000 microsteps per full step). Velocity 5 µm/s

Fig. 23 Position deviation



Fig. 24 Frequency spectrum




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5 Dynamic Position Correction

(Mapping)

Optimization of the overall accuracy of a positioning axis can

be achieved by dynamic position correction. In particularly

with rotary axes, it is possible to considerably improve the

absolute accuracy, usually by a factor of 10.

For this purpose, the deviation from the target position at a

predefined step size is initially determined with the help of a

reference measuring system. A system with an accuracy of

±0.2 arcsec is available for this purpose at PI miCos. The

measured deviations are stored in the controller (SMC Hydra)

as a correction table.

Dynamic correction then takes place during operation be-

cause the values are already being used in the profile genera-

tor for calculation of the motion profile. That means all abso-

lute errors are actually corrected during motion.

Fig. 29 The absolute accuracy of a PRS-110 (now L-611) rotation stage

with stepper motor and angle-measuring system. The deviation

from the target position is determined in steps of 1°. The angular er-

ror can be up to ±0.004°

Fig. 30 The measured values from fig. 29 were stored in the controller

(SMC Hydra) and used for dynamic position correction. The symmet-

rical behavior independent of the direction of rotation is clearly visi-

ble. It was possible to considerable reduce the position deviation

and is maximum ±0.0003°

Fig. 31 The bidirectional repeatability is considerably and permanent-

ly improved by the stored error correction (mapping). The meas-

urement shows several repetitions in steps of 10° in both the posi-

tive and negative direction of rotation


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6 Measurement Set-Up

6.1 Ambient conditions, and resources

All measurements were performed in a measurement labora-

tory under standard laboratory conditions, i.e., clean sur-

roundings without cleanroom classification, room tempera-

ture 22°C ±1°C, air humidity 43% ±3%. The measurement set-

up is on a table isolated from vibration without further provi-

sion for isolation from thermal, acoustic or other external

influences.

Measuring device, linear: Renishaw XL-80 interferometer

Measuring device, rotational: Heidenhain RON-905

Height of the reference mirror above the motion platform:

25 mm

Fig. 32 Noise measurements from the SMC Hydra controller. Axis at

rest, energized and controlled (sample frequency 10 kHz, unfil-

tered). The noise level is at approximately 3 nm (peak-peak), which

can be attributed to the interferometer

Basically, the ambient conditions influence the achievable

precision during positioning. A fluctuation of the ambient

temperature of only 0.01 °C already has an effect of around

10 nm on the thermal expansion of a stage made of alumi-

num. Stabilization of the surroundings is therefore a basic

requirement for precision and the repeatability of the results.

If required, ultraprecision axes with special material pairing

can be used, for example, on a granite base.

6.2 Positioning Systems and Motion Con-

trollers

Measuring was performed on standard linear and rotation

positioning systems, partly with additionally integrated meas-

uring systems. Stages from series production were used.

The following positioning systems were tested:

L-511 (formerly LS-110)

L-509 (formerly PLS-85)

L-611 (formerly PRS-110)

The motor controllers or motion controllers are also from the

PI portfolio.

Fig. 33 SMC Hydra with integrated DeltaStar Eco encoder interface

module. 3000 microsteps per full step, evaluation from analog posi-

tion signals (sin/cos, 1 Vpp)

Fig. 34 C-663.11 Mercury Step; 16 microsteps per full step, without

position control


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Authors

Joachim Oberfell has been working for the former miCos Gmbh, now

PI miCos GmbH, for more than 20 years

He is a specialist for complex positioning tasks and has fre-

quently proved his particular talent for optimizing positioning

systems and motion controllers. A sympathetic ear for cus-

tomer requirements and his profound knowledge on motion

control merge to produce the ideal solution for the respective

application. Of course, it goes without saying that the precise

knowledge of the operating conditions is an important re-

quirement.

Joachim Oberfell attaches great importance to understanding

the way a motor controller works in order to exploit all possi-

bilities that a positioning system has to offer, whether it be a

high-precision application in basic research such as coordina-

tion of several axes in Beamline experiments, or an ideal

solution in the automation of production systems, where

industry controllers with robust positioning axes are trans-

formed to high-tech applications with future potential.

Birgit Schulze is product manager at Physik Instrumente (PI)

About PI

Over the past four decades, PI (Physik Instrumente) with

headquarters in Karlsruhe, Germany, has become the leading

manufacturer of positioning systems with accuracies in the

nanometer range. The privately managed company is repre-

sented at four locations in Germany and internationally by

fifteen sales and service subsidiaries. More than 850 highly

qualified employees all over the world enable the PI Group to

fulfill virtually any requirement in the field of innovative

precision positioning technology. All key technologies are

developed in-house. This allows the company to control every

step of the process, from design to shipment: The precision

mechanics and electronics as well as position sensors.

The required piezoceramic elements are manufactured by

PI Ceramic, our subsidiary in Lederhose, Germany, one of the

global leaders for piezo actuator and sensor products.

PI miCos GmbH in Eschbach near Freiburg, Germany, special-

izes in positioning systems for ultrahigh vacuum applications

and parallel-kinematic positioning systems with six degrees of

freedom as well as custom-made designs.

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performance of stepper motor axes · 2020. 8. 4. · stepper motor controllers with more microsteps...

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